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Optics and Spectroscopy

Correlation of light beams in a transparent medium with cubic nonlinearity and their amplification

В. Н. Горбачев, Andrew I. Trubilko

Published Sep 1, 2000• 0 citations
Publisher

Abstract

Propagation of two waves in a transparent one-dimensional medium with cubic nonlinearity is analyzed. Correlation between the two beams develops, which periodically changes with the length of a medium and is quantum or classical in nature. Mutual correlation between the waves in this medium may be enhanced without destruction in the resonant one-photon amplification process.

DOI
10.1134/1.1310705

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Propagation of two waves in a transparent one-dimensional medium with cubic nonlinearity is analyzed. Correlation between the two beams develops, which periodically changes with the length of a medium and is quantum or classical in nature. Mutual correlation between the waves in this medium may be enhanced without destruction in the resonant one-photon amplification process.
Optical processes in which the quantum correlations of squeezed light in an entangled state of the type of an Einstein-Podolsky-Rosen pair or a Greenberger-Horne-Zeilinger triplet will be conserved in consequence of the presence of integrals of motion are considered. For the cases of parametric three-photon interaction in a transparent nonlinear medium and of resonant interaction with an atomic ensemble, it was found that, along with the conservation of the entangled state, the amplification of the light power arises.
The kinetic equation for the case of reflection of a broadband entangled light of a nondegenerate parametric source from a cavity is derived with the use of the technique of stochastic differential Ito equations. Statistical properties of the light reflected from a cavity with a nonlinear transparent medium, in which the process of special parametric interaction occurs, are considered on the basis of the obtained equation. Due to the integrals of motion, the entangled light, which is an EPR pair of continuous variables, can be amplified without destruction of the quantum correlation.
The quantum statistics of the light in the transparent medium with cubic nonlinearity is considered. Two types of transparent media are treated, namely, the cold transparent medium with a ground working level and the inversion-free medium with the lasing levels of the same population. The spectra of light fluctuation are found on the basis of both Scully-Lamb and Haken theories. The conditions for the use of effective Hamiltonian are determined. Basing on the exact solution of the Fokker-Plank equation for the Glauber-Sudarshan P-function the inversion-free medium with cubic nonlinearity is shown to be the source of spontaneous radiation with non-Gaussian statistics.
We consider propagation of a weakly nonlinear probe light beam in a resonant three-level atomic system where an optical lattice is induced by a standing-wave control field and conditions for electromagnetically induced transparency are created. We employ a unified theory to solve the respective nonlinear system of equations in various regimes and investigate formation of spatial optical solitons and instabilities, both analytically and numerically. We show that the effect of the lattice is twofold. On the one hand it allows one to reduce the probe beam intensity necessary for observation of nonlinear effects until the level of one-photon energy, and on the other hand the lattice allows for implementation of different dynamical regimes either by simple manipulation of its parameters or by varying one- and two-photon detunings or by changing the geometry of the incident probe beam.